Weird Armature Deformation
While you can rig with a Mirror modifier on your mesh, it is best in your case here to just apply it, you won't be able to rig your character properly if it is active with your current naming scheme. You might also want to then change your Pivot center from 3D Cursor to Bounding Box Center by using , (comma) or selecting it from the view header, having it set to rotate around the 3D Cursor can also lead to some weird behaviour when trying to pose if you don't know what to expect. You might also want to recalculate your mesh normals at this point with CtrlN.

…and finally, try again..

For some help in parenting the mesh to the armature, you can refer to How can I automatically generate vertex groups for an armature?. It wouldn't hurt to add some more geometry (loopcuts) to the arms and legs to help the character deform better either.